# volkov

From untb v1.6-5
by Robin K S Hankin

##### Expected frequency of species

Given a community size, biodiversity parameter $\theta$, and an immigration rate $m$, returns the expected frequency of species with $n$ individuals, for $0

- Keywords
- math

##### Usage

`volkov(J, params, bins = FALSE, give = FALSE)`

##### Arguments

- J
- Size of community
- params
- A two-element vector with first element interpreted as
theta, the Fundamental biodiversity parameter and the second, m,
interpreted as the probability of immigration. This argument will
accept the output of
`optimal.params()`

- bins
- Boolean, with default
`FALSE`

meaning to return the expected number of species with $1,2,\ldots,J$ individuals, and`FALSE`

meaning to return the binned total, using a Preston-like binning system as used in`preston(`

- give
- Boolean, with
`TRUE`

meaning to return*all*the output of`integrate()`

, and default`FALSE`

meaning to return just the value of the integral

##### Value

- Returns an object of class
phi .

##### Note

The method used is slightly inefficient: the terms to the left ofthe integral sign [in Volkov's equation 7] are integrated and this is, strictly, unnecessary as it is not a function of $y$. However, taking advantage of this fact results in messy code.

##### References

I. Volkov and others 2003.

##### See Also

##### Examples

```
volkov(J=21457,c(theta=47.226, m=0.1)) # Example in figure 1
volkov(J=20,params=c(theta=1,m=0.4))
data(butterflies)
r <- plot(preston(butterflies,n=9,orig=TRUE))
jj <- optimal.params(butterflies) # needs PARI/GP
jj <- c(9.99980936124759, 0.991791987473506)
points(r,volkov(no.of.ind(butterflies), jj, bins=TRUE),type="b")
```

*Documentation reproduced from package untb, version 1.6-5, License: GPL*

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